Comparing my logs to others for my ilevel I believe my main issue is not using Blizzard as much. I tend to only use it later on in the fight. Due to this, I believe it is affecting my dps because I am not able to cast Frozen Orb as often.

The reason I don't use Blizzard as much as others is because my guild puts a heavy emphasis on not killing the adds too early in phase 1, as tends to happen from time to time. Since my dps isn't as high as others in my guild I would think I would be able to blizzard non-stop without much of a problem to help get more frozen orb casts. However, the raid leader freaks out on me when he sees blizzard because he is afraid the adds will die too early.

Any thoughts? Am I correct on why my DPS is low or might it be something else? If I am correct, do you think I should be ok spamming blizzard without killing the adds too early?

I'm afraid that mistress is probably the worst fight to go over the damage loss. During progression I had to drop splitting ice and blizzard damage because others just deleted the adds.
Tldr unless you're assigned to pad you probably won't have comparable damage to others.

Simple answer: fight mech over dps meter in any situation. The main goal is to get the kill and of course the loot. As long as you know why your dps is low comparing yourself on ranking and parse you should not worry about it. Let the false glory of parses and ranking to the other as they rely often on not executing fights mechanics and funnelling the boss or even on fights length. Be a great raider and follow the lead of those in charge. If they are dumb enough to judge you ONLY on the number shown on the dps meter... find another raiding guild.